#1**+1 **

Note that by ASA, triangles ACN and XCN are congruent

This means that AN = XN = 5

And AN + XN = AX = 10

So...in triangle AXB.....M is the midpoint of AB and N is the midpoint of AX

But.....if these sides are split in a 1:1 ratio....then a segment connecting MN must be parallel to base BX

Therefore....we have that

AN / MN = AX / BX

5 / MN = 10 / 14

5 / MN = 5 / 7

This implies that MN = 7

CPhill Oct 10, 2018